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Any number, of yuor choice can be next. It is always possible to find a position-to-value rule in the form of a polynomial of order 5 that will fit the above values and any other value.
The polynomial of order 4 that will fit the above values is
Un = (-n4 + 10n3 - 23n2 + 14n + 24)/24 for n = 1, 2, 3, ...
and accordingly, the next number is 6.
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